. "\u041F\u0440\u043E\u0446\u0435\u0441\u0438 \u043F\u0435\u0440\u0435\u043A\u0438\u0434\u0443"@uk . . . "Umklapp scattering"@en . "In crystalline materials, Umklapp scattering (also U-process or Umklapp process) is a scattering process that results in a wave vector (usually written k) which falls outside the first Brillouin zone. If a material is periodic, it has a Brillouin zone, and any point outside the first Brillouin zone can also be expressed as a point inside the zone. So, the wave vector is then mathematically transformed to a point inside the first Brillouin zone. This transformation allows for scattering processes which would otherwise violate the conservation of momentum: two wave vectors pointing to the right can combine to create a wave vector that points to the left. This non-conservation is why crystal momentum is not a true momentum. Examples include electron-lattice potential scattering or an anharmonic phonon-phonon (or electron-phonon) scattering process, reflecting an electronic state or creating a phonon with a momentum k-vector outside the first Brillouin zone. Umklapp scattering is one process limiting the thermal conductivity in crystalline materials, the others being phonon scattering on crystal defects and at the surface of the sample. Figure 1 schematically shows the possible scattering processes of two incoming phonons with wave-vectors (k-vectors) k1 and k2 (red) creating one outgoing phonon with a wave vector k3 (blue). As long as the sum of k1 and k2 stay inside the first Brillouin zone (grey squares), k3 is the sum of the former two, thus conserving phonon momentum. This process is called normal scattering (N-process). With increasing phonon momentum and thus larger wave vectors k1 and k2, their sum might point outside the first Brillouin zone (k'3). As shown in Figure 2, k-vectors outside the first Brillouin zone are physically equivalent to vectors inside it and can be mathematically transformed into each other by the addition of a reciprocal lattice vector G. These processes are called Umklapp scattering and change the total phonon momentum. Umklapp scattering is the dominant process for electrical resistivity at low temperatures for low defect crystals (as opposed to phonon-electron scattering, which dominates at high temperatures, and high-defect lattices which lead to scattering at any temperature.) Umklapp scattering is the dominant process for thermal resistivity at high temperatures for low defect crystals. The thermal conductivity for an insulating crystal where the U-processes are dominant has 1/T dependence. The name derives from the German word umklappen (to turn over). Rudolf Peierls, in his autobiography Bird of Passage states he was the originator of this phrase and coined it during his 1929 crystal lattice studies under the tutelage of Wolfgang Pauli. Peierls wrote, \"\u2026I used the German term Umklapp (flip-over) and this rather ugly word has remained in use\u2026\". The term Umklapp appears in the 1920 paper of Wilhelm Lenz's seed paper of the Ising Model, (when Rudolph Peierls was 13 years old)."@en . . . . "1119085381"^^ . . . . . "Diffusion Umklapp"@fr . "2212817"^^ . "\u041F\u0440\u043E\u0446\u0435\u0441\u0438 \u043F\u0435\u0440\u0435\u043A\u0438\u0434\u0443 - \u043F\u0440\u043E\u0446\u0435\u0441\u0438 \u0437\u0456\u0442\u043A\u043D\u0435\u043D\u043D\u044F \u043C\u0456\u0436 \u043A\u0432\u0430\u0437\u0456\u0447\u0430\u0441\u0442\u0438\u043D\u043A\u0430\u043C\u0438 \u0432 \u043A\u0440\u0438\u0441\u0442\u0430\u043B\u0430\u0445, \u043F\u0440\u0438 \u044F\u043A\u0438\u0445 \u0437\u0430\u043A\u043E\u043D \u0437\u0431\u0435\u0440\u0435\u0436\u0435\u043D\u043D\u044F \u0456\u043C\u043F\u0443\u043B\u044C\u0441\u0443 \u0437\u0431\u0435\u0440\u0456\u0433\u0430\u0454\u0442\u044C\u0441\u044F \u0437 \u0442\u043E\u0447\u043D\u0456\u0441\u0442\u044E \u0434\u043E \u0432\u0435\u043A\u0442\u043E\u0440\u0430 \u043E\u0431\u0435\u0440\u043D\u0435\u043D\u043E\u0457 \u0491\u0440\u0430\u0442\u043A\u0438. , \u0434\u0435 - \u0437\u0432\u0435\u0434\u0435\u043D\u0430 \u0441\u0442\u0430\u043B\u0430 \u041F\u043B\u0430\u043D\u043A\u0430, - \u0441\u0443\u043C\u0430\u0440\u043D\u0438\u0439 \u043F\u043E\u0447\u0430\u0442\u043A\u043E\u0432\u0438\u0439 \u0445\u0432\u0438\u043B\u044C\u043E\u0432\u0438\u0439 \u0432\u0435\u043A\u0442\u043E\u0440 \u0443\u0441\u0456\u0445 \u043A\u0432\u0430\u0437\u0456\u0447\u0430\u0441\u0442\u0438\u043D\u043E\u043A, - \u0441\u0443\u043C\u0430\u0440\u043D\u0438\u0439 \u043A\u0456\u043D\u0446\u0435\u0432\u0438\u0439 \u0445\u0432\u0438\u043B\u044C\u043E\u0432\u0438\u0439 \u0432\u0435\u043A\u0442\u043E\u0440 \u0443\u0441\u0456\u0445 \u043A\u0432\u0430\u0437\u0456\u0447\u0430\u0441\u0442\u0438\u043D\u043E\u043A, - \u0434\u043E\u0432\u0456\u043B\u044C\u043D\u0438\u0439 \u0432\u0435\u043A\u0442\u043E\u0440 \u043E\u0431\u0435\u0440\u043D\u0435\u043D\u043E\u0457 \u0491\u0440\u0430\u0442\u043A\u0438. \u041F\u0440\u043E\u0446\u0435\u0441\u0438 \u043F\u0435\u0440\u0435\u043A\u0438\u0434\u0443 \u0432\u0430\u0436\u043B\u0438\u0432\u0456, \u043D\u0430\u043F\u0440\u0438\u043A\u043B\u0430\u0434, \u0434\u043B\u044F \u0442\u0430\u043A\u043E\u0433\u043E \u044F\u0432\u0438\u0449\u0430, \u044F\u043A \u0442\u0435\u043F\u043B\u043E\u043F\u0440\u043E\u0432\u0456\u0434\u043D\u0456\u0441\u0442\u044C \u0434\u0456\u0435\u043B\u0435\u043A\u0442\u0440\u0438\u043A\u0456\u0432. \u0417\u0430\u0432\u0434\u044F\u043A\u0438 \u0446\u0438\u043C \u043F\u0440\u043E\u0446\u0435\u0441\u0430\u043C \u043A\u0432\u0430\u0437\u0456\u0447\u0430\u0441\u0442\u0438\u043D\u043A\u0438 \u043C\u043E\u0436\u0443\u0442\u044C \u0440\u043E\u0437\u0441\u0456\u044E\u0432\u0430\u0442\u0438\u0441\u044F \u043F\u0440\u0438 \u0437\u0456\u0442\u043A\u043D\u0435\u043D\u043D\u044F\u0445 \u043D\u0430 \u0432\u0435\u043B\u0438\u043A\u0456 \u043A\u0443\u0442\u0438."@uk . . . . . . . . . "\u041F\u0440\u043E\u0446\u0435\u0441\u0438 \u043F\u0435\u0440\u0435\u043A\u0438\u0434\u0443 - \u043F\u0440\u043E\u0446\u0435\u0441\u0438 \u0437\u0456\u0442\u043A\u043D\u0435\u043D\u043D\u044F \u043C\u0456\u0436 \u043A\u0432\u0430\u0437\u0456\u0447\u0430\u0441\u0442\u0438\u043D\u043A\u0430\u043C\u0438 \u0432 \u043A\u0440\u0438\u0441\u0442\u0430\u043B\u0430\u0445, \u043F\u0440\u0438 \u044F\u043A\u0438\u0445 \u0437\u0430\u043A\u043E\u043D \u0437\u0431\u0435\u0440\u0435\u0436\u0435\u043D\u043D\u044F \u0456\u043C\u043F\u0443\u043B\u044C\u0441\u0443 \u0437\u0431\u0435\u0440\u0456\u0433\u0430\u0454\u0442\u044C\u0441\u044F \u0437 \u0442\u043E\u0447\u043D\u0456\u0441\u0442\u044E \u0434\u043E \u0432\u0435\u043A\u0442\u043E\u0440\u0430 \u043E\u0431\u0435\u0440\u043D\u0435\u043D\u043E\u0457 \u0491\u0440\u0430\u0442\u043A\u0438. , \u0434\u0435 - \u0437\u0432\u0435\u0434\u0435\u043D\u0430 \u0441\u0442\u0430\u043B\u0430 \u041F\u043B\u0430\u043D\u043A\u0430, - \u0441\u0443\u043C\u0430\u0440\u043D\u0438\u0439 \u043F\u043E\u0447\u0430\u0442\u043A\u043E\u0432\u0438\u0439 \u0445\u0432\u0438\u043B\u044C\u043E\u0432\u0438\u0439 \u0432\u0435\u043A\u0442\u043E\u0440 \u0443\u0441\u0456\u0445 \u043A\u0432\u0430\u0437\u0456\u0447\u0430\u0441\u0442\u0438\u043D\u043E\u043A, - \u0441\u0443\u043C\u0430\u0440\u043D\u0438\u0439 \u043A\u0456\u043D\u0446\u0435\u0432\u0438\u0439 \u0445\u0432\u0438\u043B\u044C\u043E\u0432\u0438\u0439 \u0432\u0435\u043A\u0442\u043E\u0440 \u0443\u0441\u0456\u0445 \u043A\u0432\u0430\u0437\u0456\u0447\u0430\u0441\u0442\u0438\u043D\u043E\u043A, - \u0434\u043E\u0432\u0456\u043B\u044C\u043D\u0438\u0439 \u0432\u0435\u043A\u0442\u043E\u0440 \u043E\u0431\u0435\u0440\u043D\u0435\u043D\u043E\u0457 \u0491\u0440\u0430\u0442\u043A\u0438. \u041F\u0440\u043E\u0446\u0435\u0441\u0438 \u043F\u0435\u0440\u0435\u043A\u0438\u0434\u0443 \u0432\u0430\u0436\u043B\u0438\u0432\u0456, \u043D\u0430\u043F\u0440\u0438\u043A\u043B\u0430\u0434, \u0434\u043B\u044F \u0442\u0430\u043A\u043E\u0433\u043E \u044F\u0432\u0438\u0449\u0430, \u044F\u043A \u0442\u0435\u043F\u043B\u043E\u043F\u0440\u043E\u0432\u0456\u0434\u043D\u0456\u0441\u0442\u044C \u0434\u0456\u0435\u043B\u0435\u043A\u0442\u0440\u0438\u043A\u0456\u0432. \u0417\u0430\u0432\u0434\u044F\u043A\u0438 \u0446\u0438\u043C \u043F\u0440\u043E\u0446\u0435\u0441\u0430\u043C \u043A\u0432\u0430\u0437\u0456\u0447\u0430\u0441\u0442\u0438\u043D\u043A\u0438 \u043C\u043E\u0436\u0443\u0442\u044C \u0440\u043E\u0437\u0441\u0456\u044E\u0432\u0430\u0442\u0438\u0441\u044F \u043F\u0440\u0438 \u0437\u0456\u0442\u043A\u043D\u0435\u043D\u043D\u044F\u0445 \u043D\u0430 \u0432\u0435\u043B\u0438\u043A\u0456 \u043A\u0443\u0442\u0438."@uk . . . . "Scattering Umklapp"@it . . "\u041F\u0440\u043E\u0446\u0435\u0441\u0441\u044B \u043F\u0435\u0440\u0435\u0431\u0440\u043E\u0441\u0430 \u2014 \u043F\u0440\u043E\u0446\u0435\u0441\u0441\u044B \u0441\u0442\u043E\u043B\u043A\u043D\u043E\u0432\u0435\u043D\u0438\u044F \u043C\u0435\u0436\u0434\u0443 \u043A\u0432\u0430\u0437\u0438\u0447\u0430\u0441\u0442\u0438\u0446\u0430\u043C\u0438 \u0432 \u043A\u0440\u0438\u0441\u0442\u0430\u043B\u043B\u0430\u0445, \u043F\u0440\u0438 \u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u0437\u0430\u043A\u043E\u043D \u0441\u043E\u0445\u0440\u0430\u043D\u0435\u043D\u0438\u044F \u0438\u043C\u043F\u0443\u043B\u044C\u0441\u0430 \u0432\u044B\u043F\u043E\u043B\u043D\u044F\u0435\u0442\u0441\u044F \u0441 \u0442\u043E\u0447\u043D\u043E\u0441\u0442\u044C\u044E \u0434\u043E \u0432\u0435\u043A\u0442\u043E\u0440\u0430 \u043E\u0431\u0440\u0430\u0442\u043D\u043E\u0439 \u0440\u0435\u0448\u0451\u0442\u043A\u0438. , \u0433\u0434\u0435 \u2014 \u043F\u043E\u0441\u0442\u043E\u044F\u043D\u043D\u0430\u044F \u041F\u043B\u0430\u043D\u043A\u0430, \u2014 \u0441\u0443\u043C\u043C\u0430\u0440\u043D\u044B\u0439 \u043D\u0430\u0447\u0430\u043B\u044C\u043D\u044B\u0439 \u0432\u043E\u043B\u043D\u043E\u0432\u043E\u0439 \u0432\u0435\u043A\u0442\u043E\u0440 \u0432\u0441\u0435\u0445 \u043A\u0432\u0430\u0437\u0438\u0447\u0430\u0441\u0442\u0438\u0446, \u2014 \u0441\u0443\u043C\u043C\u0430\u0440\u043D\u044B\u0439 \u043A\u043E\u043D\u0435\u0447\u043D\u044B\u0439 \u0432\u043E\u043B\u043D\u043E\u0432\u043E\u0439 \u0432\u0435\u043A\u0442\u043E\u0440 \u0432\u0441\u0435\u0445 \u043A\u0432\u0430\u0437\u0438\u0447\u0430\u0441\u0442\u0438\u0446, \u2014 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u043B\u044C\u043D\u044B\u0439 \u0432\u0435\u043A\u0442\u043E\u0440 \u043E\u0431\u0440\u0430\u0442\u043D\u043E\u0439 \u0440\u0435\u0448\u0451\u0442\u043A\u0438. \u041F\u0440\u043E\u0446\u0435\u0441\u0441\u044B \u043F\u0435\u0440\u0435\u0431\u0440\u043E\u0441\u0430 \u0432\u0430\u0436\u043D\u044B, \u043D\u0430\u043F\u0440\u0438\u043C\u0435\u0440, \u0434\u043B\u044F \u0442\u0430\u043A\u043E\u0433\u043E \u044F\u0432\u043B\u0435\u043D\u0438\u044F, \u043A\u0430\u043A \u0442\u0435\u043F\u043B\u043E\u043F\u0440\u043E\u0432\u043E\u0434\u043D\u043E\u0441\u0442\u044C \u0434\u0438\u044D\u043B\u0435\u043A\u0442\u0440\u0438\u043A\u043E\u0432. \u0411\u043B\u0430\u0433\u043E\u0434\u0430\u0440\u044F \u044D\u0442\u0438\u043C \u043F\u0440\u043E\u0446\u0435\u0441\u0441\u0430\u043C \u043A\u0432\u0430\u0437\u0438\u0447\u0430\u0441\u0442\u0438\u0446\u044B \u043C\u043E\u0433\u0443\u0442 \u0440\u0430\u0441\u0441\u0435\u0438\u0432\u0430\u0442\u044C\u0441\u044F \u043F\u0440\u0438 \u0441\u0442\u043E\u043B\u043A\u043D\u043E\u0432\u0435\u043D\u0438\u044F\u0445 \u043D\u0430 \u0431\u043E\u043B\u044C\u0448\u0438\u0435 \u0443\u0433\u043B\u044B."@ru . . "4731"^^ . . . . . "In crystalline materials, Umklapp scattering (also U-process or Umklapp process) is a scattering process that results in a wave vector (usually written k) which falls outside the first Brillouin zone. If a material is periodic, it has a Brillouin zone, and any point outside the first Brillouin zone can also be expressed as a point inside the zone. So, the wave vector is then mathematically transformed to a point inside the first Brillouin zone. This transformation allows for scattering processes which would otherwise violate the conservation of momentum: two wave vectors pointing to the right can combine to create a wave vector that points to the left. This non-conservation is why crystal momentum is not a true momentum."@en . "Le terme diffusion Umklapp (de l'allemand umklappen, replier) d\u00E9signe une repliement du vecteur d'onde d'un phonon sur la zone de Brillouin. Le ph\u00E9nom\u00E8ne a \u00E9t\u00E9 d\u00E9couvert par Rudolf Peierls et Wolfgang Pauli en 1929. Lors de la collision de deux phonons, les vecteurs d'onde k1 et k2 s'ajoutent. Si le vecteur r\u00E9sultant k3 sort de la zone de Brillouin, il est \u00E9quivalent \u00E0 la somme du vecteur G caract\u00E9risant le r\u00E9seau r\u00E9ciproque, et d'un vecteur k'3 inclus dans la zone et pouvant pointer dans la direction oppos\u00E9e \u00E0 k3. La conservation de l'\u00E9nergie est assur\u00E9e par ce ph\u00E9nom\u00E8ne : E(k3) = E(k3+G) mais ce processus ne conserve pas la quantit\u00E9 de mouvement, une partie \u00E9tant transf\u00E9r\u00E9e \u00E0 l'ensemble du r\u00E9seau cristalin. Ce ph\u00E9nom\u00E8ne est typique d'un repliement de spectre : l'onde correspondante \u00E0 k3 a une longueur inf\u00E9rieure \u00E0 celle de G qui repr\u00E9sente le r\u00E9seau et fait office de syst\u00E8me d'\u00E9chantillonnage. L'onde r\u00E9sultante, de longueur plus grande, a une direction quelconque, possiblement oppos\u00E9e \u00E0 celle de l'onde correspondante \u00E0 k3. Ce processus de diffusion est le facteur principal de la r\u00E9sistance thermique de conduction aux temp\u00E9ratures typiquement sup\u00E9rieures \u00E0 100 K dans les cristaux ayant peu de d\u00E9fauts. La diffusion Umklapp pr\u00E9dit une d\u00E9pendance en temp\u00E9rature de la conductivit\u00E9 thermique en 1/T."@fr . "Le terme diffusion Umklapp (de l'allemand umklappen, replier) d\u00E9signe une repliement du vecteur d'onde d'un phonon sur la zone de Brillouin. Le ph\u00E9nom\u00E8ne a \u00E9t\u00E9 d\u00E9couvert par Rudolf Peierls et Wolfgang Pauli en 1929. Lors de la collision de deux phonons, les vecteurs d'onde k1 et k2 s'ajoutent. Si le vecteur r\u00E9sultant k3 sort de la zone de Brillouin, il est \u00E9quivalent \u00E0 la somme du vecteur G caract\u00E9risant le r\u00E9seau r\u00E9ciproque, et d'un vecteur k'3 inclus dans la zone et pouvant pointer dans la direction oppos\u00E9e \u00E0 k3."@fr . . "\u041F\u0440\u043E\u0446\u0435\u0441\u0441\u044B \u043F\u0435\u0440\u0435\u0431\u0440\u043E\u0441\u0430 \u2014 \u043F\u0440\u043E\u0446\u0435\u0441\u0441\u044B \u0441\u0442\u043E\u043B\u043A\u043D\u043E\u0432\u0435\u043D\u0438\u044F \u043C\u0435\u0436\u0434\u0443 \u043A\u0432\u0430\u0437\u0438\u0447\u0430\u0441\u0442\u0438\u0446\u0430\u043C\u0438 \u0432 \u043A\u0440\u0438\u0441\u0442\u0430\u043B\u043B\u0430\u0445, \u043F\u0440\u0438 \u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u0437\u0430\u043A\u043E\u043D \u0441\u043E\u0445\u0440\u0430\u043D\u0435\u043D\u0438\u044F \u0438\u043C\u043F\u0443\u043B\u044C\u0441\u0430 \u0432\u044B\u043F\u043E\u043B\u043D\u044F\u0435\u0442\u0441\u044F \u0441 \u0442\u043E\u0447\u043D\u043E\u0441\u0442\u044C\u044E \u0434\u043E \u0432\u0435\u043A\u0442\u043E\u0440\u0430 \u043E\u0431\u0440\u0430\u0442\u043D\u043E\u0439 \u0440\u0435\u0448\u0451\u0442\u043A\u0438. , \u0433\u0434\u0435 \u2014 \u043F\u043E\u0441\u0442\u043E\u044F\u043D\u043D\u0430\u044F \u041F\u043B\u0430\u043D\u043A\u0430, \u2014 \u0441\u0443\u043C\u043C\u0430\u0440\u043D\u044B\u0439 \u043D\u0430\u0447\u0430\u043B\u044C\u043D\u044B\u0439 \u0432\u043E\u043B\u043D\u043E\u0432\u043E\u0439 \u0432\u0435\u043A\u0442\u043E\u0440 \u0432\u0441\u0435\u0445 \u043A\u0432\u0430\u0437\u0438\u0447\u0430\u0441\u0442\u0438\u0446, \u2014 \u0441\u0443\u043C\u043C\u0430\u0440\u043D\u044B\u0439 \u043A\u043E\u043D\u0435\u0447\u043D\u044B\u0439 \u0432\u043E\u043B\u043D\u043E\u0432\u043E\u0439 \u0432\u0435\u043A\u0442\u043E\u0440 \u0432\u0441\u0435\u0445 \u043A\u0432\u0430\u0437\u0438\u0447\u0430\u0441\u0442\u0438\u0446, \u2014 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u043B\u044C\u043D\u044B\u0439 \u0432\u0435\u043A\u0442\u043E\u0440 \u043E\u0431\u0440\u0430\u0442\u043D\u043E\u0439 \u0440\u0435\u0448\u0451\u0442\u043A\u0438. \u041F\u0440\u043E\u0446\u0435\u0441\u0441\u044B \u043F\u0435\u0440\u0435\u0431\u0440\u043E\u0441\u0430 \u0432\u0430\u0436\u043D\u044B, \u043D\u0430\u043F\u0440\u0438\u043C\u0435\u0440, \u0434\u043B\u044F \u0442\u0430\u043A\u043E\u0433\u043E \u044F\u0432\u043B\u0435\u043D\u0438\u044F, \u043A\u0430\u043A \u0442\u0435\u043F\u043B\u043E\u043F\u0440\u043E\u0432\u043E\u0434\u043D\u043E\u0441\u0442\u044C \u0434\u0438\u044D\u043B\u0435\u043A\u0442\u0440\u0438\u043A\u043E\u0432. \u0411\u043B\u0430\u0433\u043E\u0434\u0430\u0440\u044F \u044D\u0442\u0438\u043C \u043F\u0440\u043E\u0446\u0435\u0441\u0441\u0430\u043C \u043A\u0432\u0430\u0437\u0438\u0447\u0430\u0441\u0442\u0438\u0446\u044B \u043C\u043E\u0433\u0443\u0442 \u0440\u0430\u0441\u0441\u0435\u0438\u0432\u0430\u0442\u044C\u0441\u044F \u043F\u0440\u0438 \u0441\u0442\u043E\u043B\u043A\u043D\u043E\u0432\u0435\u043D\u0438\u044F\u0445 \u043D\u0430 \u0431\u043E\u043B\u044C\u0448\u0438\u0435 \u0443\u0433\u043B\u044B."@ru . "\u041F\u0440\u043E\u0446\u0435\u0441\u0441\u044B \u043F\u0435\u0440\u0435\u0431\u0440\u043E\u0441\u0430"@ru . . . "Umklappprozess bezeichnet in der Festk\u00F6rperphysik eine Streuung von Phononen am Gitter. Ber\u00FCcksichtigt man bei der Behandlung der Gitterschwingungen Abweichungen vom linearen Kraftgesetz zwischen den Gitteratomen, so erh\u00E4lt man eine Wechselwirkung der Phononen. Der erste anharmonische Term beschreibt die Dreiphononenprozesse. Ragt bei einem Dreiphononenprozess nun der resultierende Wellenvektor aus der ersten Brillouin-Zone heraus, so wird er reduziert um einen reziproken Gittervektor . Der diesem Gittervektor entsprechende Impuls wird dabei an das Gitter \u00FCbertragen. Es gilt also die Quasiimpulserhaltung ."@de . "\u30A6\u30E0\u30AF\u30E9\u30C3\u30D7\u6563\u4E71\uFF08\u30A6\u30E0\u30AF\u30E9\u30C3\u30D7\u3055\u3093\u3089\u3093\u3001\u82F1: Umklapp scattering\u3001U\u6563\u4E71\u3001U\u904E\u7A0B\uFF09\u3068\u306F\u3001\u30D5\u30A9\u30CE\u30F3\u6563\u4E71\u306B\u304A\u3044\u3066\u3001\u30D5\u30A9\u30CE\u30F3\u9593\u3067\u904B\u52D5\u91CF\u4FDD\u5B58\u304C\u6210\u308A\u7ACB\u305F\u306A\u3044\u6563\u4E71\u306E\u3053\u3068\u3002 \u4E00\u65B9\u3067\u30D5\u30A9\u30CE\u30F3\u9593\u3067\u904B\u52D5\u91CF\u304C\u4FDD\u5B58\u3055\u308C\u308B\u6563\u4E71\u306E\u3053\u3068\u3092\u6B63\u5E38\u6563\u4E71\uFF08\u82F1: Normal scattering, N\u6563\u4E71\u3001N\u904E\u7A0B\uFF09\u3068\u3044\u3046\u3002 \u30A6\u30E0\u30AF\u30E9\u30C3\u30D7\u6563\u4E71\u306F\u3001\u30C7\u30D0\u30A4\u6E29\u5EA6\u3088\u308A\u3082\u9AD8\u3044\u6E29\u5EA6\u3067\u983B\u7E41\u306B\u8D77\u3053\u308B\u3002"@ja . "Umklappprozess bezeichnet in der Festk\u00F6rperphysik eine Streuung von Phononen am Gitter. Ber\u00FCcksichtigt man bei der Behandlung der Gitterschwingungen Abweichungen vom linearen Kraftgesetz zwischen den Gitteratomen, so erh\u00E4lt man eine Wechselwirkung der Phononen. Der erste anharmonische Term beschreibt die Dreiphononenprozesse. Ragt bei einem Dreiphononenprozess nun der resultierende Wellenvektor aus der ersten Brillouin-Zone heraus, so wird er reduziert um einen reziproken Gittervektor . Der diesem Gittervektor entsprechende Impuls wird dabei an das Gitter \u00FCbertragen. Es gilt also die Quasiimpulserhaltung . Er wurde zuerst von Rudolf Peierls beschrieben."@de . "Umklappprozess"@de . . . . "\u30A6\u30E0\u30AF\u30E9\u30C3\u30D7\u6563\u4E71\uFF08\u30A6\u30E0\u30AF\u30E9\u30C3\u30D7\u3055\u3093\u3089\u3093\u3001\u82F1: Umklapp scattering\u3001U\u6563\u4E71\u3001U\u904E\u7A0B\uFF09\u3068\u306F\u3001\u30D5\u30A9\u30CE\u30F3\u6563\u4E71\u306B\u304A\u3044\u3066\u3001\u30D5\u30A9\u30CE\u30F3\u9593\u3067\u904B\u52D5\u91CF\u4FDD\u5B58\u304C\u6210\u308A\u7ACB\u305F\u306A\u3044\u6563\u4E71\u306E\u3053\u3068\u3002 \u4E00\u65B9\u3067\u30D5\u30A9\u30CE\u30F3\u9593\u3067\u904B\u52D5\u91CF\u304C\u4FDD\u5B58\u3055\u308C\u308B\u6563\u4E71\u306E\u3053\u3068\u3092\u6B63\u5E38\u6563\u4E71\uFF08\u82F1: Normal scattering, N\u6563\u4E71\u3001N\u904E\u7A0B\uFF09\u3068\u3044\u3046\u3002 \u30A6\u30E0\u30AF\u30E9\u30C3\u30D7\u6563\u4E71\u306F\u3001\u30C7\u30D0\u30A4\u6E29\u5EA6\u3088\u308A\u3082\u9AD8\u3044\u6E29\u5EA6\u3067\u983B\u7E41\u306B\u8D77\u3053\u308B\u3002"@ja . . . "Lo scattering Umklapp \u00E8 un processo di scattering anarmonico fonone-fonone (o elettrone-fonone), che crea un fonone con un vettore impulso k fuori dalla prima zona di Brillouin.Lo scattering Umklapp \u00E8 uno dei processi che limitano la conducibilit\u00E0 termica dei materiali cristallini, oltre allo scattering di fononi su difetti cristallini e sulla superficie del campione. La Figura 1 mostra schematicalmente i processi di scattering di due fononi in entrata con un vettore d'onda (Vettore k) k1 ek2 (rosso) che creano un fonone in uscita con un vettore d'onda k3 (blu). Fino a quando il totale di k1 e di k2 resta dentro la prima zona di Brillouin (quadrati grigi), k3 \u00E8 la somma dei due precedenti impulsi dei fononi. Questo processo \u00E8 chiamato Scattering Normale (N-process). Con l'aumento dell'impulso dei fononi e perci\u00F2 dei vettori d'onda k1 e di k2 la loro somma potrebbe uscire dalla zona di Brillouin (k'3). Come si vede dalla Figura 2, i vettori k fuori dalla prima zona di Brillouin sono fisicamente equivalenti ai vettori al suo interno e possono essere matematicalmente trasformati l'uno nell'altro con l'aggiunta di un vettore del reticolo reciproco G. Questi processi sono detti scattering Umklapp e cambiano l'impulso totale dei fononi. Il nome deriva dalla parola tedesca umklappen (rigirare). Rudolf Peierls nella sua autobiografia \"Bird of Passage\" (ISBN 0-691-08390-8) afferma di essere stato il primo a usare questo termine e di averlo coniato, quando nel 1929 studiava i reticoli cristallini sotto la tutela di Wolfgang Pauli. Peierls scrisse \"...I used the German term Umklapp (flip-over) and this rather ugly word has remained in use...\", cio\u00E8 \"...io usai il termine tedesco Umklapp e questa brutta parola \u00E8 rimasta in uso...\"."@it . . . . . . . "\u30A6\u30E0\u30AF\u30E9\u30C3\u30D7\u6563\u4E71"@ja . . . "Lo scattering Umklapp \u00E8 un processo di scattering anarmonico fonone-fonone (o elettrone-fonone), che crea un fonone con un vettore impulso k fuori dalla prima zona di Brillouin.Lo scattering Umklapp \u00E8 uno dei processi che limitano la conducibilit\u00E0 termica dei materiali cristallini, oltre allo scattering di fononi su difetti cristallini e sulla superficie del campione."@it .